Relativity and Cosmology

Motivation
I started this online lecture series to get rid of the boredom of COVID-19 home-quarantined days, as a side fun and teaching experience but it comes out to be very productive.

Overview
This online course is divided into three parts. Part 1 is based on the basic of special relativity. This section heavily relies upon the lecture series of Dr. Pervez Hoodbhoy, apart from the content on the relativistic electrodynamics, which is from chapter 12 of “Introduction to Electrodynamics (4th edition) by David J. Griffiths”. Part 2 starts from the geometry of special relativity and then we will move towards the very basics of general relativity. This part will strictly follow “A First Course in General Relativity (2nd edition) by Bernard F. Schutz”. Part 3 will be about the basics of cosmology and most probably, I will follow “Introduction to Cosmology (2nd edition) by Barbara Ryden”.

How to join?
If you want to join this lecture series, please drop an email at the following:
bilalazam31@gmail.com

Course Material and Medium of Instructions
Lecture notes of all chapters will be uploaded after every session. Medium of instructions will be Urdu.

Course Content

• Part 1: Introduction to Special Relativity
• Lecture 1: Space and Time (Lecture Notes)
• Spacetime diagrams
• Inertial frames of reference
• Galilean transformations between two inertial frames
• Galilean transformations to sound
• Galilean transformations to light
• Michelson-Morley experiment
• Lecture 2: Einstein’s Postulates (Lecture Notes)
• Time dilation
• Length contraction
• Lorentz transformations
• Lecture 3: Simultaneity and Causality (Lecture Notes)
• Simultaneity is relative
• Synchronization of clocks in inertial frames
• Lorentz transformations of intervals
• Invariant intervals
• Causality
• Lecture 4: Addition of Velocities
• Lecture 5: Scalars, Vectors and Tensors (Lecture Notes)
• Four-vectors
• Upper/lower indices and Einstein’s summation convention
• Lorentz transformations in matrix notation
• Scalars and vectors
• Some important proofs from four-vector algebra
• Tensors
• Lecture 6: Momentum and Energy (Lecture Notes)
• Proper time
• Four-velocity of a particle
• Mass and momentum in Newtonian mechanics
• Four-momentum
• Lorentz transformations of momentum and energy
• Lecture 7: Applications of Relativity (Lecture Notes)
• Relativistic kinematics
• Momentum of a free particle
• Four-force
• Lorentz transformations of four-force
• Lecture 8: Relativistic Electrodynamics (Lecture Notes)
• Magnetism as a relativistic phenomenon
• How the fields transform?
• The electromagnetic field tensor
• Four-current
• Four-potential
• Maxwell equations and covariant formalism
• Part 2: Introduction to General Relativity
• Lecture 9: The Geometry of Special Relativity-I (Lecture Notes, Video)
• Definition of an inertial observer in SR
• New units
• Spacetime diagrams
• Construction of the coordinates used by another observer
• Lecture 10: The Geometry of Special Relativity-II (Lecture Notes)
Note: PDF of this lecture includes lecture 9 too.
• Rapidity and Construction of observer coordinates
• Invariance of the interval
• Invariant hyperbolae
• Time dilation and length contraction from the spacetime diagrams
• Geometrical approach to Lorentz transformations
• The velocity composition law
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